A modal decomposition method for the analysis of long waves amplification at coastal areas

This paper presents a model for the evaluation of long waves amplification at coastal areas, based on a modal decomposition method. It is able of modelling the growth and the decay of the natural modes of the area under investigation, and their contribution to the total wave field. The model is an improvement of that developed by Bellotti et al. (2012b), that was able of calculating the frequencies and the shapes of the natural modes, but not their amplification under the action of forcing waves. Three test cases are used for the validation and to show the capabilities of the model. The first considers the long waves resonance into a long and narrow harbour/bay over a constant water depth. It is a case for which a high degree of wave trapping into the semi-enclosed coastal area is induced by the specific shape of the coastline. The second test deals with the propagation of a group of edge waves along a straight coast with a constant sloping bottom, generated in proximity of the shoreline by a special wave maker. The model in this case properly evaluates what are the edge waves modes that contribute to the total wave field. The third case involves the interaction of a solitary wave with a conical island, for which laboratory data are available. In this test a low degree of trapping exists, but it is interesting for the present aims as the propagation of the waves around the island is expected to occur under the form of wave modes partially trapped by the bathymetry i.e. edge waves, excited by the transient wave arriving from offshore. On the basis of the tests results it is shown what is the role of the more relevant natural modes in the formation of the total surface elevation.